The present invention relates to electronic magnetic compasses for use on iron body vehicles, and particularly on vehicles having two iron bodies relatively movable with respect to each other about a vertical rotary axis, such as a tank having a turret rotatable on a hull. The purpose of such compasses is to determine the magnetic heading or azimuth of the vehicle by detecting the direction of the Earth magnetic field in the horizontal plane.
Every iron body has a naturally occurring permanent magnetic field resulting from permanently magnetized crystals in the iron. This permanent magnetic field adds vectorially to the Earth's. In addition, every iron body has a variable magnetic field induced by passing through the Earth's field. This variable field is linearly related to that of the Earth and also adds vectorially to it. These two additional vector components are also detected by a magnetic compass thereby causing erroneous readings.
Since all these effects occur in a three dimensional space, they can be mathematically modeled by three dimensional vector algebra. The vector model is derived from the original description by D. Poisson published in the Memoir of the Institut de France, 1824.
This model can best be described by looking at the Earth's magnetic field from two frames of reference: the Earth frame and the vehicle frame.
If F is the vector of Earth's magnetic field strength at the compass location, then, in the Earth frame of reference with base vectors, 1n, 1e, 1v directed North, East and nadir respectively, F will be described as: EQU F=1nFn+1eFe+1vFv (1)
In the vehicle frame of reference with base vectors, 1x, 1y, 1z directed Forward, Starboard and Down respectively, F would be described as: EQU F=1xFx+1yFy+1zFz (2)
The Earth's magnetic field is also commonly described by its field strength F, its declination, and its inclination: ##EQU1##
Field strength, declination and inclination for every location can be derived from special maps or measured by special instruments.
The relation between the description of the field vector in the two frames of reference is given by the Euler relations: EQU F.sub.(x,y,z) =T.sub..phi. T.sub..theta. T.sub..PSI. F.sub.(n,e,v) ( 4)
Where .PSI.,.theta.,.phi. are the azimuth, pitch and roll angles of the vehicle and T.sub..PSI., T.sub..theta., T.sub..phi. are the respective Euler rotation matrices.
The magnetic field M at the compass location on an iron body vehicle can be described as: EQU M=H+(U'+I)T.sub..phi. T.sub..theta. T.sub..PSI. F (5)
Matrix U' provides for the effect of the vehicle's induced magnetism. Matrix I is a unity matrix providing for the original Earth magnetic field that exists at the compass location if the vehicle were made of wood. Vector H is the magnetic field caused by the permanent magnetism of the vehicle. This equation can be shortened; if we let U=U'+I, then: EQU M=H+UT.sub..phi. T.sub..theta. T.sub..PSI. F (6)
This equation gives a very accurate account of the magnetic situation of an iron body vehicle based on the assumption of linearity. In other words, it is assumed that the vehicle's iron does not become saturated at the field strength of 0.5 gauss (the Earth magnetic field strength). This assumption is justified on the basis of the types of steel used on tanks.
Poisson's original description, as set forth for example, on page 270 of the book "Magnetic Compasses and Magnetometers" by Alfred Hine, used different notations. Poisson expressed the magnetic field at the compass position of a ship by the equations: EQU X.sub.1 =X+aX+bY+cZ+P EQU Y.sub.1 =Y+dX+eY+fZ+Q EQU Z.sub.1 =Z+gX+hY+kZ+R
where X, Y and Z are three orthogonal components of the Earth's magnetic field; X.sub.1, Y.sub.1 and Z.sub.1 are three components of the total field at the compass position, directed respectively to forward, to starboard and perpendicular to the keel; a to k represent nine soft-iron rod, a mathematical conception as the rods as such have no physical existence; and P, Q and R are the components of the permanent magnetic field.
It can be readily seen that the components P, Q and R are the equivalent to the Vector H, and that the factors a to k are the equivalent of Matrix U'.
The explicit description of the Euler rotation matrices is as follows: ##EQU2##
Vector H and matrix U can also be used to describe the magnetic effects of the iron body of a tank. In this case H and U are not constant but are a function of the turret-to-hull traverse angle, indicated hereafter as Equation (6) then takes the form: EQU M=H(.alpha.)+V(.alpha.)T.sub..phi. T.sub..theta. T.sub..PSI. F (6a)
The meaning of this is that each component of "H" and "U" takes a different value for each position of the turret relative to the hull of the tank.
The inverse of equation 6a is the basic equation of the compass, namely: ##EQU3##
Vector A represents the magnetic field seen in a horizontal frame of reference at the compass location.
Equation 7 can be implemented on an analog or a digital computer to compute the magnetic azimuth or heading of a vehicle using data supplied by triaxal magnometer and a dual inclinometer or a vertical gyro.
Electronic magnetic compasses of this type are described in U.S. Pat. Nos. 3,596,069; 3,696,518 and 4,414,753; and in British Pat. No. 591,019. These patents, however, do not deal particularly with vehicles having two iron bodies relatively movable with respect to one another, such as tanks having a turret rotatable on a hull, especially the influences of the permanent and induced magnetic fields on the readings of the compass of such vehicles.
Israeli Pat. No. 64237 describes a magnetic compass particularly for vehicles having two relatively movable iron bodies, but the manner for correcting the influence of the permanent magnetic field and the induced magnetic field on the readings of the compass is different from that of the present invention, as will be described more particularly below.